I NEED HELP ASAP!!! I'LL GIVE BRAINLIEST TO THE CORRECT ANSWER!!!

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

KLnow more about coordinates here;

https://brainly.com/question/32836021

#SPJ11

The area of the triangle QRS is: 140 sq.units

The area of the triangle by box method is:

Area of triangle = Area of box rectangle - Area of 3 triangles

Thus:

Area of box rectangle = 15 * 20 = 300 sq.units

Area of small triangle 1 = ¹/₂ * 4 * 20

= 40 sq.units

Area of small triangle 2 = ¹/₂ * 11 * 15

= 82.5 sq.units

Area of small triangle 3 =  ¹/₂ * 5 * 15

= 37.5 sq.units

Thus:

Area of shaded triangle = 300 - (40 + 82.5 + 37.5)

= 140 sq.units

Read more about Area of triangle at: https://brainly.com/question/17335144

#SPJ1

Part a

\(\angle POR=\frac{\pi}{2}\) radians, so \(\theta=\frac{3}{7}(\pi/2)=\boxed{\frac{3\pi}{14}}\)

Part b

The area of sector QOR is \(\frac{1}{2}(15^2)\left(\frac{3\pi}{14} \right)=\frac{675\pi}{28}\)

The area of triangle POQ is \(\frac{1}{2}(15)(15) \sin \frac{2\pi}{7}=\frac{225}{2} \sin \frac{2\pi}{7}\)

So, the total area, in square centimeters, is \(\frac{675\pi}{28}+\frac{225}{2} \sin \frac{2\pi}{7}\)

A confidence interval cannot instantly lead to rejecting the null hypothesis in a hypothesis test. In the given case the null hypothesis is either rejected or rejected based on test statistics.

α = 0.05

μ = 2

If the confidence interval is 1.0 or 2.0, then the null hypothesis value of 2 drops exceeds the interval, this makes the data contradict the null hypothesis and may reject the null hypothesis.

This alone would not be good to decline the null theory - the conclusion to reject or not reject the null hypothesis is determined by the test statistic and the alternate p-value.

To learn more about Hypothesis

https://brainly.com/question/28920252

#SPJ4

Answer:

\(x=-3,13\)

Step-by-step explanation:

Given: \(x^2-10x=39\)

To find: solutions of the given equation

Solution:

\(x^2-10x=39\\x^2-10x-39=0\)

Write \(-10=-13+3\)

Therefore,

\(x^2-13x+3x-39=0\\x(x-13)+3(x-13)=0\\(x+3)(x-13)=0\\x=-3,13\)

So, solutions of the given equation are \(-3\) and \(13\).

The probability of obtaining a sample mean between 4.1 and 4.11 in a random sample of size 511 is 0.

To calculate the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in a discrete uniform population with x = 2.4, we can use the properties of the sample mean and the given population.

In a discrete uniform population, all values are equally likely. Since the mean of the population is x = 2.4, it implies that each value in the population is 2.4.

The sample mean is calculated by summing all selected values and dividing by the sample size. In this case, the sample size is 511.

To find the probability, we need to calculate the cumulative distribution function (CDF) for the sample mean falling between 4.1 and 4.11.

Let's denote X as the value of each individual in the population. Since X is uniformly distributed, P(X = 2.4) = 1.

The sample mean, denoted as M, is given by M = (X1 + X2 + ... + X511) / 511.

To find the probability P(4.1 < M < 4.11), we need to calculate P(M < 4.11) - P(M < 4.1).

P(M < 4.11) = P((X1 + X2 + ... + X511) / 511 < 4.11)
           = P(X1 + X2 + ... + X511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(X1 + X2 + ... + X511 < 4.1 * 511)

Since each value of X is 2.4, we can rewrite the probabilities as:

P(M < 4.11) = P((2.4 + 2.4 + ... + 2.4) < 4.11 * 511)
           = P(2.4 * 511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(2.4 * 511 < 4.1 * 511)

Now, we can calculate the probabilities:

P(M < 4.11) = P(1224.4 < 2099.71) = 1 (since 1224.4 < 2099.71)
P(M < 4.1) = P(1224.4 < 2104.1) = 1 (since 1224.4 < 2104.1)

Finally, we can calculate the probability of the sample mean falling between 4.1 and 4.11:

P(4.1 < M < 4.11) = P(M < 4.11) - P(M < 4.1)
                 = 1 - 1
                 = 0

Therefore, the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in the given discrete uniform population is 0.

Learn more about Probability click here :brainly.com/question/30034780

#SPJ11

True, Gantt charts define the dependency between project tasks before those tasks are scheduled. They display the relationships between tasks and illustrate how each task is connected to one another, which helps in identifying dependencies.

To elaborate, a Gantt chart is a visual representation of a project schedule that outlines all the tasks and activities involved in completing a project. It also highlights the dependencies between tasks, meaning that some tasks cannot begin until others are completed.

By defining these dependencies before scheduling the tasks, the project manager can ensure that the project timeline is realistic and achievable. So, to answer your question, Gantt charts do indeed define dependency between project tasks before those tasks are scheduled. By using a Gantt chart, project managers can organize and allocate resources efficiently and effectively to ensure the smooth progress of a project.

To know more about illustrate visit:-

https://brainly.com/question/31613151

#SPJ11

The correct ratio to calculate MAPE is mad / (average demand).MAPE (Mean Absolute Percentage Error) is used to calculate the average percentage difference between actual and forecasted demand. It can be represented by the following formula:

MAPE = (1/n) * ∑(|actual demand - forecast demand| / actual demand) * 100

Where n represents the number of observations or time periods. In this case, MAD (Mean Absolute Deviation) is calculated by finding the absolute difference between actual demand and forecast demand. Then, the average of these absolute differences is taken to calculate the MAD. MAD is used as the denominator in the MAPE formula to calculate the average percentage error.

The other options listed are incorrect because:rsfe / mad: This ratio will not give the correct answer because the numerator (RSFE) is not used in the MAPE formula.rsef / (average demand): This ratio does not use MAD in the denominator and is therefore not a correct way to calculate MAPE.(average demand) / mad: This ratio is the reciprocal of the correct option (c), and therefore, will give the incorrect answer. Therefore, the correct ratio to calculate MAPE is mad / (average demand).

To know more about MAPE visit-

brainly.com/question/33016379

#SPJ11

Answer:

38.25

Step-by-step explanation:

Answer:

What is the question?

Put your question in the replies of this answer and I'll gladly answer you

Step-by-step explanation:

May I have brainliest please? :)

The integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is: \(8 * (1/3)tan^2\theta(1 + tan^2\theta)^(3/2) + C\), where θ is determined by x = 2tanθ, and C represents the constant of integration

What is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function.

To integrate the function \(\int(x^3/\sqrt(x^2+4))\) dx using a trigonometric substitution, we can use the substitution x = 2tanθ. Let's go through the steps:

Substitute x = 2tanθ. This implies \(dx = 2sec^2\theta d\theta.\)

Rewrite the integral in terms of θ:

\(\int((8tan^3\theta)/(\sqrt(4tan^2\theta+4))) * 2sec^2\theta d\theta.\)

Simplify the expression inside the square root:

\(\int((8tan^3\theta)/(2sec\theta)) * 2sec^2\theta d\theta.\\\\\int(8tan^3\theta) * sec\theta d\theta.\)

Simplify further:

\(16\int tan^3\theta sec\theta d\theta.\)

Apply the trigonometric identity: \(sec^2\theta = 1 + tan^2\theta\). Rearranging, we get: \(sec\theta = \sqrt(1 + tan^2\theta).\)

Substitute \(sec\theta = \sqrt(1 + tan^2\theta)\) in the integral:

\(16\int tan^3\theta * \sqrt(1 + tan^2\theta) d\theta.\)

Let u = tanθ, which implies \(du = sec^2\theta d\theta\). We can rewrite the integral in terms of u:

\(16\int u^3 * \sqrt(1 + u^2) du.\)

Now we have a rational power of u. We can use the substitution \(v = 1 + u^2\) to simplify it:

\(v = 1 + u^2\), which implies dv = 2u du.

Rewrite the integral using v:

\(16\int (u^3 * \sqrt v) * (1/2u) dv.\\\\8\int (u^2\sqrt v) dv.\)

Simplify and integrate:

\(8\int (u^2\sqrt v) dv = 8\int(u^2 * v^{(1/2)}) dv = 8\int u^2v^{(1/2)} dv.\)

Integrate \(u^2v^{(1/2)\) with respect to v:

\(8 * (1/3)u^2v^{(3/2)} + C.\)

Replace v with \(1 + u^2\):

\(8 * (1/3)u^2(1 + u^2)^{(3/2)} + C.\)

Substitute u = tanθ back into the expression:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C.\)

So, the integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C,\)

where θ is determined by x = 2tanθ, and C represents the constant of integration

To learn more about integration visit:

https://brainly.com/question/30094386

#SPJ4

Answer:

x\(\leq\)6.8333333

Step-by-step explanation:

6x-10 must be smaller than 32

6x-10 must be 31 or below

6x can be 41 or below

so 6x\(\leq\)41

so x\(\leq\)6.83333333

The value of the element in row 1, column 1 of matrix x is; y.

According to the task content, it follows that matrix x is defined as; x= [y 4].

In essence, it follows that the matrix x contains one row and 2 columns. Therefore, the element in row 1, column 1 of matrix x is; y.

Read more on matrix;

https://brainly.com/question/1821869

#SPJ1

Answer: A

Step-by-step explanation:

12 student council members like neither bowling nor ice skating. The Option A is correct.

Let x be the number of students who like both activities.

Let y be the number of students who like bowling but not ice skating

Let z be the number of students who like ice skating but not bowling.

From the table, we know that:

y = 3z and 50% of the students like one but not both activities which means:

Solving for y and z in terms of x, we get:

y = 3z and z = 24 - x - 9

y = 3z and z = 15 - x.

Substituting equation for y + z:

y + z = 2z + y = 2(15 - x) + 3x

y + z = 30 + x.

Substituting y + z into equation for the proportion of students who like one, but not both activities we get:

(30 + x) / 72 = 0.5 which simplifies to x = 12.

Substituting x into the equations for y and z, we get y = 36 and z = 3.

So, the number of student council members who dislike both activities is:

= 72 - (x + y + z + 9)

= 72 - 60

= 12.

Read more about Proportion

brainly.com/question/1496357

#SPJ1

Answer:

105 seconds

Step-by-step explanation:

To solve this, we can set up an equation.

First, let's find how far ahead Jillian is.

15*6=90

Jillian is 90 feet ahead.

Let's name the time that Samantha walks x.

7x is the distance Samantha walks.

90+6x is the distance Jillian walks.

We want to find how many seconds they have walked when the distance is equal.

So let's form an equation.

7x=90+6x

Subtract 6x from both sides.

x=90

Samantha needs to walk 90 seconds.

Jillian started 15 seconds before that.

90+15=105

Jillian had been walking for 105 seconds when the two girls had walked the same distance.

Answer: There were 115 cats at the pet store.

Step-by-step explanation:

Hi, to answer this question we have to use proportions:

Since the number of cats to dogs at the pet store was 5 to 8.

The proportion is cats / dogs = 5/8

For 184 dogs = x / 184

Where x is the number of cats:

5/8 = x/184

Solving for x:

5/8 (184) =x

115 =x

There were 115 cats at the pet store.

Feel free to ask for more if needed or if you did not understand something.

Answer: The one on the left.

Step-by-step explanation:

There is no file, but the panda on the left is bigger.

"Centripetal is the word used to describe a vector that always points toward the centre of a circular path."

The centripetal acceleration vector is an acceleration in the radial direction that is directed towards the centre of the circular line of motion. It runs perpendicular to the linear motion, or v.

The direction of the velocity shift for a ball travelling around a curve is in the direction of the curve's centre. Centripetal acceleration is the acceleration that is directed towards the centre of a curved or circular route.

Any force that changes the path of motion towards the centre of a circular motion is known as a centripetal force. The portion of the force that produces the centripetal force is the part that is perpendicular to the velocity.

To know more about vectors:

https://brainly.com/question/13590043

#SPJ4

If W = 60,

60 / 6 + 4 = 14

14 is not equal to 5

so 60 is not a solution

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

To learn more about : radians

https://brainly.com/question/29058626

#SPJ8

The joint probability density function (pdf) of two random variables X and Y is defined as f(x,y) = 1/8,0.

This means that the probability of X and Y jointly occurring is 1/8 and the probability of them not occurring is 0.

In other words, the probability of X and Y occurring together is fixed and does not depend on the values of X and Y.

The interpretation of this joint pdf can be understood as follows:

If we take two independent samples of X and Y and plot them on a two-dimensional plane, then the probability of the two samples occurring together will always be 1/8, regardless of the values of X and Y.

In other words, the joint pdf tells us the probability of two events (in this case X and Y) occurring simultaneously.

The joint pdf is a useful tool for understanding how two random variables are related to each other, as well as the probability of their occurrence.

It also provides an insight into the behavior of the two variables and can be used to calculate the expected value, variance and covariance of the two random variables.

Learn more about joint pdf here:

https://brainly.com/question/31064509#

#SPJ11

\(4(3x + 5) - 5(8x + 2) \\ 12x + 20 - 40x - 10 \\ 12 x - 40x + 20 - 10 \\ - 28x + 10\)

The reward of 600 points will be earned by spending the amount of $300.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, Omar earns 800 reward points for spending 300 dollars.

The amount of money spent to earn 600 reward points will be calculated as,

800 reward points = $300 spending

1 reward point = $300 / 800 spending

600 reward point = ($300 x 600) / 800

600 reward points = $225

Therefore, the reward of 600 points will be earned by spending the amount of $300.

To know more about an expression follow

https://brainly.com/question/11778829

#SPJ1

Answer:

37 I think

Step-by-step explanation:

Answer:

C. 5.8

Step-by-step explanation:

We use the Pythagoras theorem here. which is a²+b²=c².

a and b are the replacements for the 5miles and  3miles here.

They are a and b because a  and b are always on the right angle side.

The longest side of this triangle is called a hypotenuse which is the c in this case.

the other sides (a and b) are called the adjacent and the opposite.

it doesn't matter if you use adjacent or opposite for a and b in this case.

the only important thing is the hypotenuse here.

So it's a²+b²=c², which is 5²+3²=c².

5² is 25 and 3² is 9, so we add them and we get 34.

so c²=34, we don't want the square on c  so we send it to 34 which becomes √34.

√34 gives us 5.8 miles which is up to just only one decimal place.

You might need to use calculators for square roots because they take long to calculate.

Since the triangles are similar thie means that:

Solving for x we have:

Therefore x=14

Answer:

Sine of an angle =

opposite / hypotenuse

I this figure

AB is the opposite which is 12

BC is the hypotenuse which is 13

sine ∅ = 12/13

Therefore the sine ratio of the angle is

12/13

Hope this helps

That we added a real number (2/3) and subtracted a real number (3), but the imaginary part of the result is still (5/3)i.

First, let me clarify what 1ị represents. In mathematics, the imaginary unit i is defined as the square root of -1. Therefore, 1ị means 1 times the imaginary unit i.

To write three more equations for 1ị that are all true and all different, we can use the fact that i satisfies the equation i^2 = -1. We can also use the fact that any multiple of i, such as 2i, 3i, and so on, is also an imaginary number. Finally, we can use the fact that adding or subtracting real numbers to or from an imaginary number does not affect the imaginary part of the number.

Here are three possible equations for 1ị:

(2 + 1/3)i = 1ị + 2i

Explanation: We can add 2 times the imaginary unit i to 1 times the imaginary unit i to get 3 times the imaginary unit i, which is equal to (2 + 1/3) times the imaginary unit i.

(-1/3)i = 1ị - 4/3i

Explanation: We can subtract 4/3 times the imaginary unit i from 1 times the imaginary unit i to get -1/3 times the imaginary unit i.

(5/3)i = 1ị + 2/3 + 3i - 3

Explanation: We can add 2/3 and 3i - 3 to 1 times the imaginary unit i to get (5/3) times the imaginary unit i. Notice that we added a real number (2/3) and subtracted a real number (3), but the imaginary part of the result is still (5/3)i.

To learn more about subtracted visit:

https://brainly.com/question/2346316

#SPJ11

Answer:

16 yards of barbed wire

Step-by-step explanation:

Length=5 yards

Width=3 yards

Perimeter of the pasture=2(length + width)

=2(5 yards +3 yards)

=2(8 yards)

=16 yards

You should order 16 yards of barbed wire for fencing the pasture